The game hit New Zealand Google several hours ago, and has made its way across the globe. Presumably it will arrive in the U.S. shortly (unless the bigshots at Google HQ are worried about stepping on the JFK anniversary?). According to Mashable, the game has been in the works for four months. The designer, Matt Cruickshank, apparently got permission from the BBC to use "authentic sound effects from the show." Chris Taylor explains how the game works:

Your goal as the Doctor is to retrieve all of the letters in "Google" and return them to your TARDIS, while avoiding the exterminating Dalek. Fall afoul of the evil Dalek and you regenerate into the next Doctor down the line.